323, APS Social Insects, Lecture 7 Kin value: relatedness, reproductive value, mating success Aims 1. To show where regression relatedness, sex-specific reproductive value, and sex-specific mating success come from and how they affect the efficiency by which one organism can transmit another's genes. 2. To begin to show how to combine these three parameters to determine the value of one organism to another (kin value) and so to determine the interests of different colony members over colony reproduction. Objectives 1. To understand in general terms what regression relatedness, sex-specific reproductive value, and sexspecific mating success mean and where they come from. 2. To understand how to combine regression relatedness, sex-specific reproductive value, and sex-specific mating success to determine kin value. Part 2 of course The opening series of lectures, which introduced the eusocial insects and provided background and introductory material in several areas of social insect biology, has now ended. The second part of the course, of which this is the first lecture, focuses on an area of biology in which social insects have made an important contribution. This is the use of inclusive fitness theory to investigate conflict and conflict resolution in social groups. This area brings together theory with experiment and data collection. The theory is often used to make predictions that can be tested by appropriate data. Although the theory is mathematical, the maths is not hard. Most things can be understood via simple algebra aided by diagrams. This area is one of the two major focuses of Professor Ratniekss research and that of his laboratory at the University of Sheffield. The Big Picture Within a colony there is typically a range of individuals that the workers can rear into reproductives: males versus females, brothers versus sons versus nephews, full sisters versus half sisters. Which of these should be reared? In the case of males versus females, in what ratio (sex ratio) should they be reared? Should workers stop each other producing males and concentrate on rearing the queens sons? What is the interest of the queen? In general, natural selection will cause a worker to rear those individuals that are best at transmitting the workers genes. These are the individuals with the greatest kin value. Kin value has three basic components: regression relatedness, sex-specific reproductive value, and sex-specific mating success. Regression relatedness Genetic relatedness can be a confusing topic. We often hear things like chimps and humans share 99% of their genes. We also share genes with bacteria. Does that mean that we are 99% related to chimps, and 10% related to bacteria? The concept of relatedness as used in the study of social behaviour and evolution only considers relatedness among members of the same population. It is meaningless to talk about relatedness between chimps and humans, even though different species have genes in common. Within the human population there are individuals of different relatedness to you. On average, your relatedness to other members of the human population is defined as 0, even though they are all humans and all have the same set of gene loci as you (though probably not the same alleles at these loci). Your relatedness to your mother and father, your son and daugher, and your full-brother and full-sister are 0.5. If you have an identical twin, or can arrange to have yourself cloned, then your relatedness to that person is 1. These relatedness values come from the probability of sharing genes identical by descent. A solid basis for understanding relatedness can be obtained by considering the regression of one individuals genotype on anothers. Some complications are introduced because male Hymenoptera are haploid and females are diploid. Work your way through the examples on the slides. You should first understand how the gradient of the gene score regression to a clonemate is 1. This is where a relatedness of 1 comes from. The average gene score gradient to randomly chosen individuals in the population is 0. This is where a relatedness of 0 comes from. From these simple examples you will be ready to understand relatedness to relatives. Finally, you will also be ready to understand why, in haplodiploids, the regression relatedness of a son to his mother is not the same as from a mother to her son. It is not essential to work through all the examples in detail. What you must do is to get a general understanding of where regression relatedness is coming from. Relatedness is usually presented as a table in a book. It is also necessary to understand, in general terms, how these values are obtained.
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APS 323, Social Insects, Lecture 7 Notation: when writing regression relatednesses in symbols or in formulae use the notation brd,i where r is the recipient, d the donor, and i the colony or colonies or population you are referring to. For example bqw,i could mean "the regression relatedness of the workers (donors) in colony i to the young queens (recipients) being reared in colony i". Because of haplodiploidy bmale,female bfemale,male so it is important to consistently put the donor second when donor and recipient are of different sexes. However, relatednesses within a sex are the same when donor and recipient are switched. For example, bdaughter,mother = bmother,daughter. Sex-specific reproductive value Do not be confused by the term sex-specific. It simply means male or female. Sex-specific reproductive value means the reproductive value of one sex versus the other. The concept of reproductive value comes from R. A. Fisher and was originally applied within sexes. In particular, the reproductive value of a young female is greater than that of an old female as the young female has more of her reproductive life ahead of her. As a result, the young female will contribute more to the future gene pool of the population than will an older female. However, are we not interested in the relative reproductive values of females or males of different ages or sizes or qualities. Rather, we are interested in the relative reproductive values of ALL the males versus ALL the females in the population in one generation to the future gene pool of that population. It turns out that in eusocial Hymenoptera the females normally contribute more than the males to the future gene pool of the population. This is because of haplodiploidy, not because of eusociality. In diploids, both sexes contribute equally. To understand this, imagine that it were possible to mark all the nuclear genes in all the females in a population with red tags that remain on those genes and their copies from generation to generation. What would we see next generation or in ten generations? In diploids, in the next generation both males and females would have 50% red genes and it would stay that way in future generations. This is because a male gets half his genes from his mother and half from his father, as does a female. (We will ignore sex chromosomes and cytoplasmic DNA.) This shows that, in diploids, the sex-specific reproductive value of ALL the males is the same as that of ALL the females. If we do the same for haplodiploids we get a different result. Because a male has no father he gets all his genes from his mother. Therefore, in the next generation all the genes in males are red. In contrast, a female gets half her genes from her mother and half from her father. In the next generation the females have half red genes. The red genes seem to be doing better. Over many generations the proportion of red genes converges to 2/3 in both sexes. This means that the females contribute 2/3 to the future gene pool of the population. Males contribute the rest, 1/3. The ratio of the sex-specific reproductive values of females to males, VF/VM, is (2/3)/(1/3) = 2. There is one other thing to consider, and it applies only to eusocial haplodiploids. If the workers produce some or all of the males, then some of the males reared in a colony may carry the genes of the queens mate(s). The workers are an in-between generation by which father males can pass on their genes via workers sons. Imagine that all the males in the population are workers sons. (This happens in only a few species.) The workers genes are half red as they get half from their mother and half from their father. Therefore, the genes in the workers sons, which have no father, are also half red. If workers produce all the males we get back to the diploid situation in which in one generation half the genes in both sexes are red. If workers produce some of the males we have an intermediate situation. The ratio of sex-specific reproductive values of females to males, VF/VM, is actually equal to 1 + p where p is the proportion of males in the population that are queens sons. The above can easily be explained using diagrams and equations to show how genes are transmitted. These are shown in the lecture slides, one of which is pasted into these lecture notes. Sex-specific mating success It is well known that different individuals can have different reproductive success. But here we are again only interested in the average mating success of one sex versus the other. Males and females may, on average, have different mating success. If 20,000 males and 10,000 queens are reared, then on average each male will father half as many offspring as a queen. The mating success is, therefore, 2 to 1 in favour of females. The theory of sex ratios is mainly based not on the numbers of individuals of...